I can't speak about earlier machines, but the first computer I programmed, the IBM 705III, had 5K BCD characters (bytes came later) whose locations were numbered 0-4,999.
We talked about the first character being at memory location 0, etc.
We never referred to bits by location in the character but rather by value - the 0 bit, the 8 bit, etc.
As far as I know, the 705III came on the scene somewhere around 1957.
Assembler language for the 705III was zero based.

Things were already confusing then tho. The two accumulators on the machine were called Accumulator 1 and Accumulator 2, rather than 0 and 1.

Nothing is easy or it wouldn't be fun!!